The evolution of computer technology has resulted in the creation of a sophisticated technical art devoted to the representation of graphical information generated by computers. This art is referred to as computer graphics. In recent years, the use of three-dimensional computer graphics in scientific and engineering applications has increased, along with the demand for realistic images.
Besides lines, markers and polygons, computer graphics displays today support more general geometric parameters, such as parametric surfaces. An example of parametric surfaces includes non-uniform rational B-spline surfaces which are useful in CAD/CAM applications in representing objects such as automobile fenders and the like. Parametric surfaces can be either untrimmed or trimmed to accommodate irregular edges, holes and intersections with other surfaces.
Parametric surfaces may be represented as a quadrilateral mesh, in which the mesh is a two-dimensional array of points. However, for trimmed surfaces, the quadrilateral mesh representation has previously been problematic since areas along the trimmed surfaces are normally tessellated into discrete polygons with variable detail in the tessellation around the areas of the trimming curve intersection. In other words, certain areas of the trimming curve would be tessellated further such that additional points would be generated which need to be evaluated. This causes a decrease in efficiency and system performance because the advantages of the regular mesh are lost.
Therefore, a need exists for a method and system for representing a trimmed parametric surface as a quadrilateral mesh, such that the mesh in most cases, can maintain the same number of points. A need also exists for a method and system for representing a trimmed parametric surface wherein system performance and efficiency is not degraded. A need further exists for a technique for representing a trimmed parametric surface wherein the points of an array representing the parametric surface coincide with the points of the trimming polylines. Further, a technique for representing a trimmed parametric surface is needed, wherein the rendering hardware is capable of making a distinction between included and excluded areas.